
Interpretability of machine-learned results.
In the practical sense, we should address the interpretability of results collected from machine learning, e.g., ground for estimations and uncertainty quantification. Also, in fluid dynamics fields, some researchers have tackled this issue: Maulik et al. [1]} have recently demonstrated the capability of probabilistic neural network (PNN) with a problem setting of POD coefficient prediction over a time of shallow water equation, vortex shedding behind a cylinder or an airfoil, and NOAA sea surface temperature. One of beauties in their work is that the PNN can tell us a confidence interval in estimating target attributes.
Otherwise, Jagodinski et al. [2]} used a three-dimensional CNN with gradient-weighted class activation mapping (Grad-CAM) [3]}, [4]} to identify the important area for the prediction of ejection events in a turbulent channel flow. In addition, Kim and Lee [5]} examined the relationship between the estimation of the wall-normal heat flux and vortical motion of turbulent channel flow by looking inside CNN.

Amount of training data.
To extract the underlying physics of fluid flow data, massive amount of training data has been utilized for neural networks [6]}. For example, Fukami et al. [7]} reported that approximately 15 days are required to train their neural network to perform three-dimensional spatio-temporal super-resolution analysis. To reduce the computational cost and storage, a proper method to bulk out the training data while keeping the ability of neural networks is eagerly desired for the fluid dynamics problems.

Generalizability of neural networks for fluid flows
A generalized model beyond various kinds of flows is also one key factor toward next steps of machine learning and fluid dynamics. Some studies have recently examined this point to consider inter/extrapolation boundary in terms of training data. Hasegawa et al. [8]} examined the Reynolds number dependence in performing CNN-LSTM-based reduced order modeling considering a laminar cylinder wake. They also investigated the generalizability of geometric variation using the similar form of reduced order surrogate [9]}. Otherwise, Erichson et al. [10]} used an MLP referred to as shallow decoder to reconstruct fluid flows from local sensor measurements and discussed for inter/extrapolation of training data by considering two dimensional forced turbulence.

